Topological Field Theory and Stochastic Dynamics

[2608.15220] Topological Field Theory and Stochastic Dynamics Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Theory arXiv:2608.15220 (hep-th) [Submitted on 15 Aug 2026] Title: Topological Field Theory and Stochastic Dynamics Authors: Igor V. Ovchinnikov View a PDF of the paper titled Topological Field Theory and Stochastic Dynamics, by Igor V. Ovchinnikov View PDF HTML (experimental) Abstract: In the late 1980s, Baulieu and Grossman demonstrated that the supersymmetric formulation of Langevin stochastic differential equations (SDEs), proposed earlier by Parisi and Sourlas, belongs to the family of Witten-type topological field theories (TFTs). From a certain angle, this finding may appear puzzling: TFTs have no local degrees of freedom, whereas SDEs do exhibit local fluctuations. In this paper, we address this apparent contradiction in the context of the supersymmetric theory of stochastic dynamics (STS), a generalization of the Parisi-Sourlas-Baulieu-Grossman approach to SDEs of arbitrary form. We further discuss how, within STS, dynamical chaos can be identified with the spontaneous breakdown of the corresponding topological supersymmetry, while 1/f noise can be understood as a consequence of the Goldstone theorem. The butterfly effect, in turn, calls for an effective field-theoretic description that may itself possess a hidden topological structure, as we speculate on the basis of the Ginzburg-Landau approach and insights from AdS/CFT duality. Comments: RevTex4.2, 24 pages, 1 figure Subjects: High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph); Algebraic Topology (math.AT); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2608.15220 [hep-th] (or arXiv:2608.15220v1 [hep-th] for this version) https://doi.org/10.48550/arXiv.2608.15220 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Nucl. Phys. B 1030 (2026) 117620 Related DOI : https://doi.org/10.1016/j.nuclphysb.2026.117620 Focus to learn more DOI(s) linking to related resources Submission history From: Igor Ovchinnikov V. [ view email ] [v1] Sat, 15 Aug 2026 13:14:07 UTC (205 KB) Full-text links: Access Paper: View a PDF of the paper titled Topological Field Theory and Stochastic Dynamics, by Igor V. Ovchinnikov View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-08 Change to browse by: math math-ph math.AT math.DS math.MP nlin nlin.CD References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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